In my case, the "glitches" were so frequent that the Nisley code linked above never worked. No entire minute was observed to pass without at least one bad pulse. I do have commercial WWVB clocks in the house that keep perfect time, so it is not a hopeless situation.
I too could see the signal pulses using an LED, (using a simple transistor driver directly from the radio output) so there is no doubt about receiving the proper 60 kHz WWVB signal.
My idea was to implement a 1-second phase locked loop synchronized to the ticks, and then simply poll the input very frequently to determine the pulse width.